Pretty sure there's no way of getting from Ukraine to the UK without passing through at least one country (possibly even multiple) which do have centers that it's possible to apply for UK visas in - not since their airspace closed to commercial traffic at the start of the war at least.
I wonder if there is a high demand in any of these countries that could cause delays in getting these processed.
The application is made online, then you book and attend an appointment at a Visa Application Centre in one of the following locations:
Budapest, Hungary
Chisinau, Moldova
Warsaw, Poland
Bucharest, Romania
Paris, France
Flights in Ukraine have been suspended, you will have to travel through one of these cities anyway.